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The phrase "with the norm" is grammatically correct and can be used in written English.
It is often used to indicate conformity or adherence to a standard or expected behavior. Here are a few examples: - "Our company aims to always be in line with the norm when it comes to sustainable practices." - "The students were praised for their exemplary behavior, which was in line with the norm for our school." - "Although his actions may seem unconventional, they are actually in line with the norm in his culture." - "The new policy is in accordance with the norm set by industry leaders." - "It is important for businesses to operate with the norm in mind to ensure fair competition."
Exact(60)
Let Y denote a normed space with the norm | ⋅ |.
Let X denote a normed space equipped with the norm | ⋅ |.
Let X be a normed vector space with the norm ∥ ⋅ ∥.
From then on I never wanted to fit in with the norm".
with the norm (3.2).
endowed with the norm.
where, with the norm (1.9).
endowed with the norm (2.2).
equipped with the norm (2.5).
Let with the norm (1.3).
where is with the norm.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com